Are there things Elixir can do that Erlang cannot, or vice versa?

You shouldn’t stumble on anything you can do in one that you can’t in the other, since you can freely call Elixir code from Erlang and vice-versa. You can even easily mix Erlang and Elixir files in one project.

In Elixir:

:erlang_module.erlang_function(args)

in Erlang:

'Elixir.ElixirModule':elixir_function(args)